Solution: Random Pick with Weight

Let's solve the Random Pick with Weight problem using the Modified Binary Search pattern.


You’re given an array of positive integers, weights, where weights[i] is the weight of the ithi^{th} index.

Write a function, Pick Index(), which performs weighted random selection to return an index from the weights array. The larger the value of weights[i], the heavier the weight is, and the higher the chances of its index being picked.

Suppose that the array consists of the weights [12,84,35][12, 84, 35]. In this case, the probabilities of picking the indexes will be as follows:

  • Index 0: 12/(12+84+35)=9.2%12/(12 + 84 + 35) = 9.2\%

  • Index 1: 84/(12+84+35)=64.1%84/(12 + 84 + 35) = 64.1\%

  • Index 2: 35/(12+84+35)=26.7%35/(12 + 84 + 35) = 26.7\%


  • 11 \leq weights.length 104\leq 10^4

  • 11 \leq weights[i] 105\leq 10^5

  • Pick Index() will be called at most 10410^4 times.

Note: Since we’re randomly choosing from the options, there is no guarantee that in any specific run of the program, any of the elements will be selected with the exact expected frequency.

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